If this author was a Mafia gangster

If this author was a Mafia gangster

If the author was a Mafia gangster, a really smooth big-time operator who had to hire a full time personal attorney to defend him from diverse criminal charges, he might admonish his lawyer: “I do not need you to tell me so very simply just exactly what I can and cannot do. I want you to advise me precisely how to do what I want! Capisci?”

Now, the author concedes that GR, as it is most commonly interpreted, regards the hyperbolic black hole gravitational field as impossible. But as a system of sixteen complicated simultaneous nonlinear homogeneous partial differential equations - correct him if he is wrong, his having never actually done this - one must make some assumptions and define some boundary conditions in order just to begin to solve them. When this is done, one determines only the coefficients of these equations, many of which will be zero if one is lucky. The remainder will sum to at least one additional partial differential equation, whereupon more of the terms may cancel and drop out, especially after we apply “suitable” multipliers. This simplifying process is one of the main goals of many of the assumptions and boundary conditions and without which the equations might be unsolvable.

Often, the simplifying assumptions and the artificial boundary conditions may amount to gross oversimplification.

This final differential equation(s) must still be solved (integrated) and so, even more assumptions and boundary conditions must be assigned in order to do so. When this is done shrewdly, the equations can indeed be solved whereupon the results are equations that can be regarded as a set of physical rules that can be tested experimentally or observationally. Like the Friedmann equations under the FLRW metric.

The author finds it difficult to believe that there is no way to select assumptions and define boundary conditions realistically in such a way as to permit the hyperbolic black hole gravitational field. This, especially when, in the case of the Friedmann equations for example, there happens to be a parameter designated ρ/ρ_crit which determines whether the whole universe is spherical (closed), flat (perfectly Euclidian in both time and space) or hyperbolic (open).

The author knows that this is not quite relevant, so please do not focus on this stupid little example and try to tear it to pieces. But, this is mentioned just to show that one can redirect solutions of GR toward hyperbolic results so very easily just by means of solutions having some mere adjustable parameters.

Einstein cannot have been so inflexible that he would have written a theory that could be so rigidly used to prohibit reality. Such a prohibition would be a XXX atrocity wrought by a Grade AAA genius! Ha Ha!

Let us not promulgate or propagate any such atrocities of our own.

Author’s challenge: a case of fine Spanish wine (NOT Italian; capisci?) to the understanding personality who can help him find a way to “force” GR to do want he wants! I am a biased scientist. But, at least I admit it.

In the meantime, all he is saying below is that there is sufficient reason to go ahead and allow the hyperbolic field as a postulate. The ideas below are not meant to be picked apart and eaten alive. But, they should still be digested. They are not logically necessary and sufficient, so demolishing them may be pointless. They are meant only to illustrate the notion that to allow the hyperbolic field as a postulate might make good practical sense.

As acknowledged above, the hyperbolic black hole gravitational field (HBHF) is said to be prohibited by common very reasonable interpretations of general relativity. But, the consequences of finding some realistic loophole, some valid formulation of the HBHF are potentially momentous. They may even be capable of causing a revolutionary paradigm shift in the science of cosmology. Reasons that could motivate the search for some means to validate the HBHF are manifold.

1.) The HBHF field can explain the anomalous orbital velocity distribution of stars in galaxies.

2.) The HBHF can explain anomalous velocity distributions of galaxies in galactic clusters.

3.) HBHFs can explain the dependencies and magnitudes of the Sunyaev-Zeldovich effect. It can even explain the progressive changes in the SZ differential redshift offset effects that are seen when this phenomenon is observed to occur through large voids closer and closer to Earth.

4.) The HBHF can explain the apparent offsets in the barycenters of colliding galactic clusters – the so-called “Bullet Cluster effect”.

5.) The peculiar galactic thermal distribution effects can be traced to the HBHF.

6.) The HBHF can more fully explain gravitational lensing phenomena.

7.) The HBHF can explain the inhomogeneity that is seen to have developed in the early universe, said inhomogeneity having been present since before the time of “recombination” of electrons with atomic nuclei. (This inhomogeneity probably persisted as the hot plasma produced from the Big Bang “recombined” to produce now greatly redshifted emission of the cosmic microwave background radiation (CMB). Acoustic variation and long prior quantum perturbations are said to have been insufficient to fully account for the deviations that are now observed in the CMB.)

8.) The HBHF process in 7.) can provide a confirmatory rationale for the Inflation theory of cosmogenesis. An Inflationary Big Bang, with the “inflaton” behaving like a hyper-massive, decaying, excited, quantum, fundamental point particle might have resulted in a large number of big primordial black holes as well as a lot of electromagnetic energy and many subatomic particles. This decay debris as these primordial black holes, with their super-extensive hyperbolic gravitational fields, would serve to induce an unusually broad gravitational “halo” effect similar to the one postulated for Dark Matter that is supposed to have been largely responsible for the inhomogeneity observed today in the CMB and in the actual observed distribution of galaxies.

9.) An extension of the HBHF hypothesis to the whole universe can provide a mechanism for a positive lambda in the LCDM Friedmann model of the universe. But, the label “lambda cold dark matter” might be replaced by the “lambda apparent cold dark matter” or LACDM model, since “cold dark matter” will then have been seen to be utterly superfluous.

One angle to deal with criticism along the lines of Birkhoff’s Theorem and its siblings might be to postulate that a black hole is wholly a quantum object so that its gravitational field is really a quantum field of a different form from the kind of gravity in GR. Perhaps Alan Guth’s “inflaton field” is related to gravity, but being hyper-excited is not actually gravity, exactly. And, it could have a hyperbolic normalizable form because it originates, not in a Hugh Everett style meta-universe, but in an “infra-universe” or “sub-space” of fewer dimensions.

So, even according to present interpretations of GR, it could then indeed be hyperbolic in its mathematical description. This “Many Worlds” interpretation of the nature of black holes and/or the Inflaton Particle may include laws of physics that no longer pertain except in regard to black holes, especially since black holes involve physically real singularities. Inside black holes, the laws of physics not only may break down (so it is impossible to say what rules may be valid and what rules are struck down), but may be delocalized outside the singularity and even far outside the event horizon. And, yes, the author knows that he speaks of black holes and the whole universe in the same breath.

After all, if the universe was once a quantum entity, then it still is. Macroscopic quantum effects should still be discernable in larger systems than in just tiny globs of Bose-Einstein condensates. Would super-massive black holes be large enough for you? Yuk Yuk!

The contention that some future theory of quantum gravity will erase the physically real singularities in black holes is like a dream. The author thinks that theoretical physicists have been thrashing around for long enough. It is time to acknowledge that no such TOE or GUT will be forthcoming. No GUT has been proposed that uniquely and competently predicts anything new that has actually been verified, is falsifiable and actually unifies what it claims to unify.

So yes, a theory of quantum gravity has an anticipated feature wherein it will not result in any singularities or event horizons. And thus, it will have no black holes. But, there is a catch:

Recently, attention has been drawn to the fuzzball model in string theory. Based on calculations for particular situations, the hypothesis suggests that, in general, the individual states of a black hole solution might not have an event horizon or singularity. But, for an actual observer, the statistical average of such states may appear just like an ordinary black hole in the lenses of general relativity.

(to be continued)